Lemma 3.4 ([1]}, Proposition 7.1.)
Let \(P(z)\)  be a nonzero polynomial of degree \(q\ge 5\)  without multiple zeros whose derivative is given by
\(P^{\prime }(z)=q(z-d_{1})^{q_{1}}(z-d_{2})^{q_{2}},\) 
